Patterns and Numbers in Nature PDF

Patterns and Numbers IN NATURE WHAT DOES MATHEMATICS HAVE TO DO WITH NATURE? WHAT MATHEMATICS IS ABOUT AND WHAT IT IS FOR? WHAT MATHEMATICS IS AOUT AND WHAT IT IS FOR? PATTERNS PATTERNS if u cut it into half parehas lang itsura...

Patterns and Numbers IN NATURE WHAT DOES MATHEMATICS HAVE TO DO WITH NATURE? WHAT MATHEMATICS IS ABOUT AND WHAT IT IS FOR? WHAT MATHEMATICS IS AOUT AND WHAT IT IS FOR? PATTERNS PATTERNS if u cut it into half parehas lang itsura self similar, isa lang itsura tas paulit i ulit paulit ulit na itsura that keeps on any cracks sa bato or wht repeating like tiles sa bahay like sa zebra curvy, bendy like water flow sa mga kanal foamy like sa sabon, sa ibabaw ng drinks like coke,coffee any stripes yung may mga gitna, like typhoon, flower petals anything yung lumaki like katol 1.Symmetry a. Reflection or Bilateral b. Radial Symmetry c. Translational Symmetry 2. Fractals 3. Spirals 4. Spots and Stripes 5. Flower Petals 6. Number Patterns and Sequences Mathematics for our World  Application of Mathematics in our World Mathematics helps organize patterns and regularities in the world; Application of Mathematics in our World Mathematics helps predict behavior of nature and phenomena Application of Mathematics in our World Mathematics helps control nature and occurence in the world for our own good Application of Mathematics in our World Mathematics has applications in many human endeavors making it indispensable Fibona most famous for the Fibonacci sequence, SEQUENCE cci Fibona SEQUENCE cci from smaller number to bigger number Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE Fibonacci SEQUENCE  Golde Fibonacci Sequence and the Golden Ratio n RATIO 1.618 A remarkable property of the sequence is that the ratio between two numbers in the sequence eventually approaches the “Golden Ratio” as a limit. 1/1=1 2/1=2 3/2=1.5 5/3=1.6667 8/5=1.6 13/8=1.625 21/13=1.6154  Golde Fibonacci Sequence and the Golden Ratio n RATIO RATIO = 1.618 OR 0.618 ~ REPRESENTED BY THE GREEK LETTER PHI ~ PHI EQUALS ± 1.6180339887 … AND ± 0.6180339887 … ~ RATIO OF PHI IS 1 : 1.618 OR 0.618 : 1 ~ MATHEMATICAL DEFINITION IS PHI2 = PHI + 1 ~ EUCLID SHOWED HOW TO FIND THE GOLDEN  Golde Fibonacci Sequence and the Golden Ratio n RATIO Golden Rectangles can be found in playing cards, windows, book covers, file cards, ancient buildings, and modern skyscrapers. Many artists have incorporated the Golden Rectangle into their works because of its aesthetic appeal. Some researchers believe that classical Greek sculptures of the human body were proportioned so that the ratio of the total height to the height of the navel was the Golden Ratio. Golde GOLDEN REACTANGLE n RATIO  Golde Fibonacci Sequence and the Golden Ratio nRATIO Golden Ratio: When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio "φ" which is approximately 1.618034... In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:  X6 (1.618 ) 6 - (1- 1 618) 6 Golde Fibonacci Sequence and the Golden Ratio nRATIO Using The Golden Ratio to The answer comes out as a Calculate Fibonacci whole number equal to the Numbers addition of the previous two terms. And even more surprising is that we can calculate any Example: Find x6 and X12 Fibonacci Number using the Golden Ratio: Golde THE GOLDEN SECTION AND GEOMETRY nRATIO ~ IS THE RATIO OF THE SIDE OF A REGULAR PENTAGON TO ITS DIAGONAL ~ THE DIAGONALS CUT EACH OTHER WITH THE GOLDEN RATIO ~ PENTAGRAM DESCRIBES A STAR THAT FORMS PARTS OF MANY FLAGS Golde THE GOLDEN SECTION IN ARCHITECTURE nRATIO ~ GOLDEN SECTION APPEARS IN MANY OF THE PROPORTIONS OF THE PARTHENON IN GREECE ~ FRONT ELEVATION IS BUILT ON THE GOLDEN SECTION (0.618 TIMES AS WIDE AS IT IS TALL)  Golde THE GOLDEN SECTION IN MUSIC nRATIO ~ STRADIVARI USED THE GOLDEN SECTION TO PLACE THE F-HOLES IN HIS FAMOUS VIOLINS ~ BAGINSKY USED THE GOLDEN SECTION TO CONSTRUCT THE CONTOUR AND ARCH OF VIOLINS Golde THE GOLDEN SECTION IN HUMAN nRATIO Golde THE GOLDEN SECTION IN FASHION nRATIO Golde THE GOLDEN SECTION IN FASHION nRATIO Golde THE GOLDEN SECTION IN PLANTS nRATIO 1. TIME MANAGMENT 2.MEASUREMENT 3. BUDGETTING 4. 5.FINANCE PLANNING WHY MATH IS INDISPENSIBLE?